Relief among investors that Italian populists had failed to form a government quickly gave way on Monday to concerns that new elections could become a vote on the future of the euro.

Italian President Sergio Mattarella on Sunday refused to accept the nomination of a euroskeptic finance minister, prompting the anti-establishment Five Star Movement and far-right League party to give up trying to form an administration, at least for now.

The euro edged higher early Monday along with Italian stocks and government bonds. They had come under heavy pressure in recent weeks because of fears that the populist parties' program of €100 billion ($118 billion) in tax cuts and spending pledges could leave Italy in breach of rules governing the European currency.

"Mattarella has made it clear that he will not allow any policy that could put Italy on a slippery slope towards a major confrontation with the [European Union] that could potentially jeopardize Italy's euro membership," wrote Holger Schmieding, chief economist at Berenberg bank, in a research note on Monday.

Related: The three biggest risks to global investors

But the market gains evaporated quickly as investors focused on an uncertain future for Italy, a founding member of the euro currency and its third largest economy.

The main Italian stock market index was down by about 2.5% in late afternoon trading.

"The electoral process is back to square one with a lot of ill will," said Kit Juckes, a currency strategist at Societe Generale. "New elections are now more likely ... and the election itself is in danger of turning into a de facto referendum on euro membership."

Years of stagnation and a lack of reform have pushed Italy's government debt above €2 trillion euros ($2.3 trillion), equivalent to more than 130% of annual economic output. That's the third highest level of indebtedness in the world after Japan and Greece.

Related: Japan's longest growth streak in decades has come to an end

Protecting the 'savings of Italians'

Mattarella said it was his duty to block the finance minister's appointment to protect the "savings of Italians."

"The uncertainty in our position in the euro has alarmed international and Italian investors and savers, who have invested in our government bonds and in our industries," Mattarella said Sunday.

"The surge of the [bond] spread, day after day, increases our public debt and it reduces government spending on social programs. The losses in the the stock market, day after day, burn the resources and savings of our industries and of those who have invested. And they amount to concrete risks for our fellow citizens and for Italian families," he added.

Italy has been without a government since elections in March. Former International Monetary Fund official Carlo Cottarelli will now lead a caretaker administration until new elections later this year or in early 2019.

As a country that uses the euro, Italy has agreed to abide by EU budget rules designed to keep the currency stable. During the March election campaign, the populist parties called for those rules to be scrapped and talked about holding a referendum on the euro or leaving the European Union.

Those explosive pledges were missing from their draft government program, but analysts say they could now be revived as the populist parties blame Italy's political establishment for denying them the right to govern.

"It is also likely that the next election campaign will feature significantly stronger anti euro and euroskeptic tones," wrote Wolfango Piccoli, co-founder of Teneo Intelligence, in a research note Sunday.

"The League leader Matteo Salvini has already said that the next vote will be a 'referendum' to free Italy from the 'slavery regime' imposed by the [eurozone], Berlin, the markets and the [bond] spread," he added.

Related: 'Impossible position': Brexit is going nowhere fast

Too big to fail?

There's a huge amount at stake for Italy, and Europe.

Ratings agency Moody's warned Friday it could cut Italy's credit rating -- already just two notches above "junk" status -- because the populists' plans risked weakening its fiscal position and stalling efforts to reform the economy.

A rating downgrade would make it more costly for the Italian government to service its debts and raise the cost of new borrowing. Italy plans to issue about 250 billion euros ($292 billion) in bonds this year, according to Reuters.

Related: Turkey's economy at risk as currency hits record low

Unlike Greece, which is just beginning to emerge from eight years of international bailouts, the Italian economy is big enough to throw the entire eurozone into disarray if it suffers a debt crisis. It accounts for about 15% of eurozone GDP and 23% of the region's government debt. Greece has just over 3% of eurozone public debt.

A louder campaign in Italy against Europe will keep investors on edge.

"Even if the immediate risk of having a euroskeptic finance minister in Italy has now been at least postponed, Italian uncertainties will continue to weigh heavily on sentiment in Italy and -- to a lesser extent -- its eurozone neighbors in coming months," wrote Berenberg's Schmieding.